Manual computing device

ABSTRACT

A manual computing device is disclosed in which tokens representing abstract numerical quantities are moved with respect to each other to perform arithmetical processes. An elemental structure comprising a specific arrangement of such tokens according to the invention is described. Various combinations including such elemental structure are disclosed and a preferred color code for use on the tokens of such combinations is described.

United States Patent Wilson Sept. 5, 1972 [54] MANUAL COMPUTING DEVICE 2,654,164 10/1953 Seidenberg ..35/33 [72] Inventor: Henry Allen Wilson, 81 Atherton Ave., Atherton, Calif. 94025 [22] Filed: March 9, 1970 FOREIGN PATENTS OR APPLICATIONS 148 110 12/1936 Austria ..35/32 7 70 [211 NO 1 3 413,406 5/1925 Germany ..35/33 Related US. Application Data Primary Examiner-Wm. H. Grieb [63] g rgy fi 'g g of Attorney-Mellin, Moore and Weissenberger ,3. an one 57 ABSTRACT [52] US Cl ..35/33 1 511 Int. Cl. ..G06c 1/00 A manual computmg devlce 1S lry'whlch [58] Field of Search ..35/32, 33, 35 A tokens represemmg abstract numeflcal quantifies are moved with respect to each other to perform [56] References Cited arithmetical processes. An elemental structure comprising a specific arrangement of such tokens accord- UNITED STATES PATENTS ing to the invention is described. Various combinations including such elemental structure are disclosed 2,41 COhe-n and a p f d co o c f use on tha tokens of 22 g l i i l i such combinations is described. ar e a. 3,387,392 6/1968 Kurz ..35/33 10 Claims, 16 Drawing Figures PNENYED SEP 5 m2 SHEEI 1 OF 5 FIG 4 INVENTOR. HENRY ALLEN W|LSON FIG 5 FIGJA MENTEDSEP 8 2 3.688.418

SHEEY 2 UF 5 7| INVENTOR.

HENRY ALLEN WILSON WWW/WWW ATTORNEYS PATENTEDSEP' 5 I972 SHEET 3 BF 5 FIGJO PATENTEDSEP 51972 SHEET 0F 5 gal PHENTEDSEP 5mm 3.888.418

sum 5 or s HENRY ALLEN WILSON F|G |4 BY WWVW ATTORNEYS MANUAL COMPUTING DEVICE CROSS-REFERENCE TO RELATED APPLICATION This application is a continuation-in-part of my copending application Ser. No. 881,732, entitled Manual Computing Device, filed Dec. 3, 1969 now abandoned.

BACKGROUND OF THE INVENTION This invention relates to manual computing devices in which abstract numbers are represented by physical tokens, arithmetical processes being performed by manually moving such tokens with respect to each other, and particularly to such a device which not only facilitates the teaching of the various numerical concepts and arithmetical processes but also provides greater flexibility in the performance of such processes.

The concept of performing arithmetical processes by manually moving physical tokens representative of abstract numbers with respect to each other is very ancient. A wide variety of devices based on this concept, which devices have come to be classified generically under the name abaci, have evolved from an origin which is generally attributed to the early Greeks. In any event, abaci of many types were widely used throughout the civilized world until the advent of the Hindu-Arabic system of number notation in Western Europe. Because of the fact that arithmetical process can be written with less difiiculty using the Hindu- Arabic system of number notation as compared to older systems of numeral notation, such as Roman numerals, for example, the use of abaci was slowly abandoned in Western Europe in favor of pencil and paper. However, abaci are still widely used in Asia where cumbersome systems of numeral notation are prevalent, the two most common devices being the so-called Abacus identified with China and the so-called Soroban identified with Japan.

Thus, the Hindu-Arabic system of numeral notation enables a permanent record to be made of intermediate steps in an arithmetic process, as with pencil and paper, whereas in the use of abaci, such intermediate steps are usually obliterated by subsequent steps of the process. A price is paid for such convenience, however, in terms of a certain rigidity and inflexibility in numerical concepts and methods of practicing arithmetical processes. Such rigidity and inflexibility is imposed by the fact that all arithmetic processes involve not only action but also memory" as to prior actions taken. Thus, stylized systems of performing most arithmetical processes with pencil and paper in Hindu-Arabic numerals have been devised to reduce the requirements imposed on human memory. The net result has been to substitute the requirement for memorizing rules for practicing a wide variety of artificial arithmetic processes for the requirement of remembering past arithmetic actions. Some humans have difficulty conceptualizing the symbolism of Hindu-Arabic numerals, others have difficulty grasping the principles of the artificial arithmetic processes, still others have difficulty memorizing rules and yet others simply find it difficult to use pencil and paper. Thus, it is an object of this invention to provide a manual computing device which will minimize the requirements placed on human memory, aid in the conceptualization of abstract numbers, and allow greater flexibility in the practice of arithmetic processes.

In the use of abaci action and memory are physically combined in the manual movement of the tokens with respect to each other thus eliminating the need to remember past actions" and reducing the number of rules which must be memorized in order to practice various arithmetical processes. In fact, the advent of mechanical and electronic computers which also physically combine action and memory and are thus merely sophisticated abaci) has re-emphasized that there are only two basic arithmetical processes, namely, addition and subtraction. Multiplication, for example, may be performed by multiple addition and, similarly, division may be performed by multiple subtraction, both being subject to appropriate rules for the placement of the decimal point in the answer.

In addition to their inherent speed, accuracy and ability to make a permanent record of intermediate steps in an arithmetic process, mechanical and electronic computers have the additional advantage over the modern abacus or soroban of greater flexibility in mode of performing arithmetical processes due to the fact that both the abacus and the soroban are physically stylized. To a certain extent such stylization has been useful in that the accurate operation of an abacus or soroban depends heavily on the skill of the operator, which skill can only be acquired through repetitive operation of a particular physical structure. However, individuals have become so skilled in the operation of the abacus or soroban as to approach the speed and accuracy of mechanical computers, if not electronic computers. Thus it has been found that a simple, inexpensive, and highly portable device such as an abacus or soroban in the hands of an intelligent human can compete favorably with expensive and sophisticated machines such as mechanical and electronic computers in certain situations.

Thus, it is another object of this invention to provide a manual computing device of the abaci type offering greater flexibility in the performance of arithmetical processes than the modern abacus or soroban.

Finally, there are many situations in which an individual must perform arithmetical processes without the aid of pencil and paper due to a physical environment which makes the use of pencil and paper inconvenient. For example, in walking about in a supermarket purchasing items, it is often desirable to know the total cost of a number of such items, but inconvenient to use pencil and paper to record and total such costs.

Thus, it is yet another object of this invention to provide a portable manual computing device that may be used to record numerical quantities and perform arithmetical processes thereon under environmental conditions that would make the use of pencil and paper inconvenient.

DESCRIPTION OF THE DRAWING These and other objects and features of this invention will be more clearly apparent when the following detailed description of preferred embodiments thereof is read in conjunction with the attached drawing wherein:

FIG. 1 is a plan view of an element of a device embodying this invention;

FIG. 1A is a cross-sectional view taken along line 1A1A of FIG. 1;

FIG. 2 is a plan view of the element shown in FIG. I depicting a particular orientation of the movable tokens thereof;

FIG. 3 is a further plan view of the element shown in FIG. 1 depicting another orientation of the movable tokens thereof;

FIG. 4 is a plan view of an embodiment of this invention in which a plurality of elements such as shown in FIG. 1 are used in combination;

FIG. 5 is a plan view of the embodiment shown in FIG. 4 depicting a particular orientation of the movable tokens thereof;

FIG. 6 is a plan view of a soroban embodying features of this invention;

FIG. 7 is a plan view of an abacus embodying features of this invention;

FIG. 8 is a plan view of a further embodiment of this invention;

FIG. 9 is an elevational view of a portion of a support rod which may be used in the various embodiments of this invention; and

FIG. 10 is a cross-sectional view taken along line I010 of FIG. 9

FIG. 1 1 is a fragmentary plan view of a modification of the element of a device embodying this invention shown in FIG. 1;

FIG. 12 is a fragmentary plan view of the element shown in FIG. 11 depicting a particular orientation of the movable tokens thereof;

FIG. 13 is a plan view of a modification of the soroban shown in FIG. 6;

FIG. 14 is a plan view of a modification of the abacus shown in FIG. 7;

FIG. 15 is a plan view of a modification of the embodiment of this invention shown in FIG. 8.

DESCRIPTION OF PREFERRED EMBODIMENTS Referring to FIG. 1, a basic element of a computing device according to this invention is shown. Such basic element comprises a plurality of physical tokens 21 arranged in three groups, each group being located in a different one of three physically distinct areas or sections 22, 23 and 24. The tokens of the group in each area are mounted for movement toward and away from the other tokens and preferably toward and away from the other groups of tokens. According to this invention there are at least four and no more than five tokens located in a first one 23 of the three physically distinct areas. Similarly, there are at least four and no more than six tokens in the group located in an area 22 on one side of the first area 23 and there are at least three and no more than four tokens in the group located in area 24 on the other side of the first area 23.

According to this embodiment of the invention the tokens of all of the groups are mounted for movement along a common rectilinear path. For example, as shown in FIG. I the tokens 21 may be apertured and threaded on a rod 25 which rod 25 provides the common rectilinear path. The rod 25 is divided into three physically distinct lengths by means of a pair of web members 26 and 27 through which rod 25 passes. The ends of rod 25 are mounted in supporting members 28. As shown in FIG. IA web members 26 and 27 and supporting members 28 may be mounted on a base member 30.

It will be understood that the rod 25 could be actually divided into three distinct portions individually mounted in end-to-end relation by means of supports such as web members 26 and 27 and end supports 28. It will also be understood that many other structures could be used for mounting tokens 21 for rectilinear movement along a common path toward and away from each other, as by providing a trough arrangement or by supporting the tokens at their edges in guide means. The important aspect of this invention is that the tokens are mounted in three groups each located in a different one of three physically distinct areas and movable along a common path toward and away from each other.

According to this embodiment each of the five tokens of the group located in end area 22 represents a numerical quantity of unity or one. Each of the tokens of the group located in the middle area 23 represents the numerical quantity five and each of the four tokens in the group located in the other end area 24 represents the numerical quantity twenty-five. As shown in FIG. 1, the tokens of all the groups are located in their 0" or set" position. As in the operation of the usual abaci, various numerical quantities are represented by moving the tokens 21 to the opposite extreme location in their associated area from their 0 or set" location. Thus, referring to FIG. 2, the numerical quantity thirty-one is represented by moving a token located in the unity area 22 into abutment with web 26, moving a token located in the fives area 23 into abutment with the web 26 and moving a token located in the twenty-fives area into abutment with the web 27. Similarly referring to FIG. 3, by moving all of the tokens of each group to the opposite location in their associated area from the 0" or set" location the numerical quantity is represented. Thus, it will be seen that any numerical quantity between 0 and I30 may be represented by the appropriate location of the various tokens of each of the groups within its associated area.

At this point attention is directed to the crosshatching representing the colors of the various tokens 21. According to this invention, the color red is associated with the abstract concept of the numerical quantity one, the color white with numerical quantity 2, and color blue with numerical quantity 3, the color brown with numerical quantity 4 and the color black with numerical quantity 5. Other colors are associated with the abstract concept of numerical quantities 6 through 10 as will be described hereinafter in connection with FIGS. 6 and 8. There are, of course, other color codes associated with numerical quantities l to 10 such as the color code used on electrical resistances and capacitances to designate the value thereof. However, the color code selected for association with the abstract numerical quantities I through 10 as described herein has been specifically selected in the belief that it is particularly suited for use in teaching the basic principles of numeral notation and arithmetic processes.

Thus, the element 20 shown in FIG. I is primarily useful as a means of teaching numerical concepts and basic arithmetic processes. The student is first taught to count from I to 5 using the tokens in the end area 22. The student will quickly learn to associate the colors red, white, blue, brown and black with numerical quantitles 1, 2, 3, 4 and 5, respectively, by moving the tokens located in section 22 sequentially from the positions shown in FIG. I to the positions shown in FIG. 3.

The student is then taught to record the number of times that he has counted from I to 5 (as described above) by moving the tokens located in the middle section 23. Thus the student will quickly learn to associate each of the tokens located in the middle section 23 with the numerical quantity 5. Due to the color code the student will also quickly appreciate the concept of one group of 5", two groups of 5", three groups of 5", etc. Once the concept of numerical groups has been conceptualized as described above it is an easy step for the student to associate each of the tokens of the group located. in the other end section 24 with the numerical quantity 25 and to use such tokens to record the number of times that all tokens in the middle group have been moved to the position indicated in FIG. 3. Thus by repeated counting from one to 130 using the element 20 shown in FIG. 1, the student will quickly learn to associate both color and area location of physical tokens, which he can see and feel, with numerical quantities and numerical groups.

The next step in the teaching process is to teach the student simple addition and subtraction. It will be seen that a certain flexibility in the performance of addition and subtraction is provided, even by the single element 20 as shown in FIG. 1, in that certain numerical quantities may be represented in more than one way. Thus, a numerical quantity that is any multiple of 5 may be represented in at least two ways and a numerical quantity that is any multiple of 25 may be represented in three ways. The advantage of this flexibility will become more apparent from a consideration of the embodiment of this invention shown in FIGS. 4 and 5.

The embodiment of this invention as shown in FIG. 4 comprises a plurality of elements, such as that shown in FIG. 1, arranged in parallel array. Thus, as shown in FIG. 4, this embodiment of the invention may comprise a frame 40 which may be generally rectangular and having mounted therein four rods 41-44. The rods 41-44 are parallel to each other and equally spaced from each other. Two partitions 45 and 46 extending across the frame transversely of the rods 4144 divide the rods into three physically distinct lengths. Groups of tokens 21 are movably mounted along each of such lengths of each rod as described in connection with FIG. 1. According to this embodiment of the invention the tokens on the various lengths of the rod 41 located to the right as shown in FIG. 4 represent numerical quantities of unity, 5 and 25, respectively, as described in connection with the embodiment shown in FIG. 1. The tokens located along the various lengths of the next adjacent rod 42 represent numerical quantities ten, fifty and 250, respectively. Similarly the tokens on the next adjacent rod 43 represent numerical quantities of 100, 500 and 2,500, respectively, the tokens on the left hand rod 44 representing numerical quantities 1,000, 5,000 and 25,000, respectively. Thus according to this embodiment of the invention it would be possible to count sequentially from 1 to l44,430 by moving the tokens as described in connection with the elements shown in FIG. 1. However, it will be seen that many numerical quantities can be represented in a number of difierent ways and in counting from I to 144,430 there is no one required progression in the movement of tokens from one rod to the next, since certain of the tokens need not be used. Thus the stylization inherent in modern forms of abaci is avoided, and a much greater flexibility introduced, enabling various numerical quantities to be added to other numerical quantities in a number of different ways. However, the tokens on the various rods of the device shown in FIG. 4 may be moved or cleared" to a given position for reading when a given arithmetic process is completed. This may be accomplished by transferring the representation of all numerical quantities possible from right to left on the rods of the device. Thus as shown in FIG. 5 the numerical value 142,679 is represented by the position of the tokens. The numerical quantity 9 is represented by the position of the tokens on the right hand rod, the numerical quantity by the position of the tokens on the next adjacent rod, the numerical quantity 12,600 is represented by the tokens on the next adjacent rod and finally the numerical quantity one hundred and thirty thousand is represented by the position of the tokens on the right hand rod. These numerical quantities when added produce the total l42,679.

It is obviously difficult to give a more detailed description of the operation of the embodiment of this invention shown in FIGS. 4 and 5 without unduly multiplying drawings and words. It is believed that the following discussion of one application for the embodiment of the invention shown in FIGS. 4 and 5 will provide an adequate understanding of the usefulness and operation thereof. According to this application of the embodiment of the invention shown in FIG. 4 tokens mounted on the right hand rod 41 represent 1 cent, 5 cents and 25 cents respectively. The tokens on the next adjacent rod 42 represent 10 cents, 50 cents and $2.50, respectively. The tokens on the next adjacent rod 43 represent $1, $5 and $25, respectively, and finally the tokens on the left hand rod 44 represent $l0, $50 and $250, respectively. Thus, it will be seen that a total of I30 cents or $1.30 may be represented by moving all the tokens on the right hand rod to their indicating position. Similarly, a total of $13 may be represented by moving all of the tokens of the next adjacent rod to their indicating position, a total of may be represented by moving all of the tokens of the next adjacent rod to their indicating position and finally a total of $1,300 may be represented by moving all of the tokens on the right hand rod to their indicating position. By moving all of the tokens on all of the rods to their indicating position a total of $1,444.30 may be represented on the device shown in FIGS. 4 and 5. Assuming that the device shown in FIGS. 4 and 5 is shown at substantially full size, it will be seen that it may be easily carried in one hand. Thus it would be convenient to carry the device shown in FIGS. 4 and 5 during the course of a visit to a supermarket. As each article is purchased the price of that article may be easily recorded on the device shown in FIGS. 4 and 5. Furthermore, a number of similar numerical quantities may be repeatedly recorded on the device shown in FIGS. 4 and 5 without the necessity for clearing the device to the right. In other words, thirteen items each having a price of $9.99 could be recorded on the device before it would be necessary to clear the rods to the left in order to record additional prices. Since the digits of prices will each average less than 9 in normal use, it will be seen that it will ordinarily be possible to record to prices without any necessity for clearing to the left until the total is desired.

For this application of the invention it is necessary to provide means for preventing the tokens on the various rods from being moved accidentally during handling. In fact, the provision of such a means is desirable, if not necessary, in all of the applications for all of the devices according to this invention as described herein. Thus, referring to FIGS. 9 and 10, a preferred means is shown whereby tokens may be held against accidental movement and yet allowed to move when such movement is desired. As shown in FIG. 9 a special rod may be used in any of the embodiments of this invention disclosed herein. Such special rod 25' may be made of plastic or metal, for example, and is provided with a plurality of flexible fingers spaced along one side thereof. Such fingers project away from the center of the rod a distance greater than the radius of the aperture in the tokens to be threaded on the rod. The ends of such fingers 50 may be spaced from each other a distance approximately equal to the width of the tokens, thus allowing a token to lie at rest therebetween. The dimensions of the fingers are selected so that the fingers possess sufficient rigidity to maintain the mass of the tokens in position under conditions of acceleration present in normal handling and yet are sufficiently flexible to allow the tokens to be easily moved by hand. It is not necessary that the fingers be spaced by an amount sufficient to accommodate a token. If the fingers are made flexible enough, it is acceptable to have a large number of such fingers contained within the aperture of the tokens and butting against the inner surface of such aperture in order to retain the token in position during normal handling by means of the friction produced by the impingement ofsuch fingers thereon.

Referring to FIG. 10 it will be seen that the fingers 50 may be easily formed on the rods 25' by die-forming techniques. Thus as shown in FIG. 10 one side of the rod is simply flattened by means of an appropriate pressure die which causes the material thereof to flow up into a rib 50'. Such die member may also be provided with appropriate means to divide the rib 50 into a plurality of fingers 50. However, it is also possible to form the fingers 50 by means of cutting operations after the formation of the rib 50.

It will be understood that the tokens of the embodiment of this invention shown in FIGS. 4 and 5 are preferably colored according to the code described in connection with FIGS. 1 to 3. It will also be understood that the color of corresponding tokens on each rod will be the same. It is believed that the concept of coloring the tokens according to rank has not been used heretofore in the prior art. Thus, one feature of the invention disclosed herein is the concept of coloring the tokens of abaci according to rank. Referring to FIG. 6 it will be seen that the color code according to this invention may be readily applied to the Japanese soroban and, as shown in FIG. 7, the color code according to this invention may be readily applied to the Chinese abacus. However, it will be noted that there is a subtle difference in the color coding as applied to the soroban and abacus from the color coding as applied to the emtokens, in the soroban and abacus the color code is not repeated in the different groups. In other words, the token 61 of the soroban representing the numerical quantity five is colored black even though it is located in a different area from tokens representing numerical quantities one through four and which are colored red, white, blue and brown respectively. Similarly referring to FIG. 7 the tokens 71 representing the numerical quantity five are colored black in spite of the fact that there are two such tokens 71 in one group and one such token 71 in the other group on each rod. It will be seen that it would be more consistent with the hankus for the tokens 71 of the abacus which are included in the second group on each rod to be colored red and white and this, of course, could be done within the scope of the teaching of this invention. However, for the soroban and abacus it is preferred to use the color code in the arrangement as shown in FIGS. 6 and 7 respectively since it is believed that less confusion in the mind of the user will result therefrom.

Referring to FIG. 8 a further embodiment of this invention is shown wherein a hankus is used in combination with a pair of Chinese abaci. It will be understood that a pair of sorobans could also be used in place of the pair of Chinese abaci. As shown in FIG. 8, the hankus is located at the bottom and is separated from the first abacus by a section or physically distinct length of rods 25 on each of which is mounted a single token. Similarly the first abacus is separated from the second abacus by a section or length of rods 25 on each of which is located a single token. A similar section or length of rods 25 each having a single token mounted thereon is provided at the upper end of rods 25 above the second abacus. Thus the embodiment of this invention shown in FIG. 8 provides a complete computer which may be conveniently used for addition, subtraction, multiplication and division. The hankus comprising sections 80, and 80 may be used for the performance of addition and subtraction operations as described in connection with FIGS. 1 through 5. The abacus comprising sections 82, 82' and the abacus comprising sections 84 and 84' may be used to record the multiplier and multiplicand in multiplication processes. It will be seen that in the performance of multiplication processes the products of a plurality of multiplication processes may be recorded on the hankus for subsequent addition and each intermediate step in a multiplication process may be easily added onto the product produced by prior steps in the multiplication process. Such process may be carried on according to file and it is the function of the tokens mounted within sections 81, 83 and 85 to assist in treating the various files in order during the performance of multiplication processes. Thus the single tokens mounted on each rod in compartments or lengths 81, 83 and 85 may be moved to an appropriate location in order to 9 keep track of the particular point which has been reached in a multiplication process. Similarly in the performance of division processes the divisor and the dividend may be set up on the abaci 82, 82 and 84, 84', respectively, and the answer may be recorded on the hankus 80, 80', 80".

It is not possible to present herein an exhaustive presentation of the operation of the embodiment of this invention shown in FIG. 8. Instead it is believed that those skilled in the art will devise many modes of operation thereof which will provide substantial advantages over any mode of operation possible with abaci of the prior art. Certainly it is apparent that complicated problems involving addition, subtraction, multiplication and division may be readily carried out on the embodiment of this invention shown in FIG. 8 without the need for auxiliary recording of the results of any of the individual processes or the intermediate steps of processes.

In order to assist the operator of the device shown in FIG. 8 in keeping the value of the various files in mind, the colors of the single tokens mounted in sections or lengths 81, 83 and 85 are color coded in accordance with the teaching of this invention. Such color code beginning at the right comprises the colors red, white, blue, brown, black, pink, purple, orange, green and yellow, said colors being associated with the abstract numerical concepts 1 to 10, respectively, in the order given. As shown in FIG. 6, it is also possible to apply this color code to the rods themselves in order to assist the operator of the device in keeping his file values straight. As mentioned above, it is within the teaching of this invention to use some other color code for the file values as represented by the single tokens in sections or lengths 81, 83 and 85 or on the rods 25. For example, the color code commonly used to identify values of various electrical and electronic components, such as resistors and capacitors, could be used.

Referring to FIGS. 11 15 further embodiments of this invention are shown in which the representation of the numerical quantity by means of a physical token 21' is utilized. Thus, in FIG. 11 a fragment of an element 20' similar to the element 20 shown in FIG. 1 is depicted. Such fragment shows that the lower end area or section 22' of the element 20' has one more token 21' mounted therein than is mounted in the lower area or section 22 of element 20. Since element 20' is otherwise identical to element 20, the same reference numerals are used in both FIGS. 1 and 11 to identify corresponding parts.

FIG. 11 shows the tokens 21 and 21' of the element 20' in their set" or not in use position, whereas FIG. 12 shows the first token 21 in the lower section 22' of the element 20' moved into abutment with partition 26 to indicate the numerical quantity 0. It will be seen that the numerical quantity 0" cannot be positively represented ori the element 20 of FIG. 1 separate from the set" or not in use" position of tokens 21, since movement of the first token 21 into abutment with the partition 26 as shown in FIG. 2 represents the numerical quantity l Thus, the element 20' shown in FIGS. 11 and 12 will be useful in teaching the difference between the concepts of nothingness" as represented by the set or not in use position of FIG. 11 and the numerical quantity 0" as represented in FIG. l2.

The importance of such difference is not great in mere counting operations or simple addition and subtraction operations such as may be performed on the element 20 of FIG. 1-3 or the device of FIGS. 4 and 5 as described hereinabove. However, anyone who has used a soroban or an abacus as shown in FIGS. 6 and 7 to multiply or divide will immediately recognize the advantage of being able to distinguish between the numerical quantity 0 and a mere nothingness or not in use indication. Thus, FIG. 13 shows a soroban and FIG. 14 shows an abacus, each modified in accordance with the teaching of this invention by the addition of a physical token representative of the numerical quantity 0. In order to multiply on a soroban or abacus, the tokens on a first set of rods thereof are positioned to represent the multiplier and the tokens of a second set of rods are used for the multiplicand with the answer being recorded on the tokens of a third set of rods. The various sets of rods chosen for representation of the multiplier, multiplicand and answer are separated from each other by one or more rods which are simply not in use. However, if any one or more of the multiplier, multiplicand and answer include the numerical quantity 0 as a digit thereof, it becomes necessary for the operator to make a mental distinction between those rods which are simply not in use and those rods on which the numerical quantity 0 is represented since the positioning of the tokens will be the same in both cases. The same imposition is made upon the memory of the operator in the performance of division operations where the divisor, dividend or answer include the numerical quantity 0 as a digit or digits thereof. Thus, as shown in FIGS. 13 and 14, those rods which are in use but on which the numerical quantity 0 is represented are physically identified by the movement of the first token 21' in the lower section into its indicating position.

The distinction between nothingness" or not in use and the physical representation of the numerical quantity 0" is even more important in devices embodying a hankus where addition, subtraction, multiplication and division operations may be carried out more or less simultaneously on a single device as described above. Thus, in FIG. 15 there is shown a device including a hankus 90, 20 and in combination with a pair of abaci 92, 92' and 94, 94', all of which include a token 21 for physical representation of the numerical quantity 0".

As shown by the cross-hatching in FIGS. 12-15, the token 21' representative of the numerical quantity 0 is preferably given the same coloration as is associated with the numerical concept 10 according to the preferred color code described hereinabove. Thus, devices made in accordance with this invention are inherently suited for use with the decimal series embodied in the Hindu-Arabic system of number notation.

To this end, the device shown in FIG. 15 embodies a further modification from that shown in FIG. 8, in that the three right hand rods thereof are adapted to represent decimal places if desired. Thus, the fourth token from the right in sections 91, 93 and 95 of the device shown in FIG. 15 are colored red to represent numerical quantity 1", according to the preferred color code described above, with the tokens on the left side thereof colored in ascending order and those on the right side in descending order therefrom in accordance with such preferred color code as shown. Thus, decimals to three places may be conveniently represented according to this embodiment. The same modification is shown for the Soroban of FIG. 13 and the abacus of FIG. 14 wherein the rods are color coded as indicated to enable a number to be conveniently represented to three decimal places.

It will be understood that embodiments of the sorobans of FIGS. 6 and 13, the abacus of FIG. 7 and 14 and the devices including the hankus of FIGS. 8 and 15 will preferably have more rods than it is convenient to show in the drawing. For example, a preferred embodiment of the device shown in FIG. 15 would include twenty-seven rods with the color code offset as described above to enable a number to be conveniently represented to six decimal places.

It will also be understood that it may be found convenient to use only a portion of the preferred color code described hereinabove. For example, it will be seen that only those colors associated with the numerical quantities and l are used on the elements of FIGS. 11 and 12 and on the tokens of the soroban of FIG. 13 and abacus of FIG. 14. Thus, the coloration of the rods of such soroban and abacus could be changed to represent a repeating series from 1 to 5 with the yellow substituted for black on the evennumbered occurrence of a 5 representation. In this regard it will be noted that the simplest embodiment of this invention would be a unit consisting only of the lower area 22 or 22' of elements 20 and 21' which would find use in teaching preschool age children, for example, to count and thereby inculcate the basic color code for numerical quantities O and l-5 described above. It is interesting to note that these numerical quantities occur far more frequently in actual experience than do the numerical quantities 640".

According to a still further feature of this invention physical indicia, as distinguished from the color code described above, may be used on the tokens of embodiments thereof. For example, raised ridges might be formed on the tokens in the patterns formed by the cross-hatching lines used in the drawing hereof to represent various colors. This may be easily accomplished where the tokens are plastic beads, for example, during the manufacture of such beads. The use of such physical indicia, as distinguished from optical indicia, will serve as an aid to blind operators of devices embodying this invention and may prove useful even to sighted operators particularly when the devices must be used under poor lighting conditions.

Thus it will be seen that a new and useful device is provided for which many modes of operation may be developed by mathematicians. For example, it is believed that the Trachtenberg method of mathematical calculation may offer interesting approaches to the performance of arithmetical processes on the embodiments of this invention shown in FIGS. 8 and 15. Therefore the purpose of this application is not to obtain protection with respect to any particular mode of operation of embodiments of this invention, but rather to obtain protection with respect to the physical features of this invention. It will be seen that various features of this invention may be used in combination or certain of such features may be used alone. Therefore the various specific features of this invention and combination thereof for which protection is sought herein are specifically set forth and distinctly claimed in the following claims.

What is claimed is:

1. A manual computing device including in combination in a common frame a plurality of computing elements, each of said computing elements comprising a plurality of movable tokens arranged in three discrete groups, said tokens of each group being mounted for movement toward and away from the others of said groups within a discrete length of a rectilinear path common to all of said tokens of said element, the first of said groups including at least four and no more than six of said plurality of tokens, the second of said groups including at least four and no more than five of said plurality of tokens, the third of said groups including at least three and no more than four of said plurality of tokens, said second group of tokens being interposed between said first group and said third group of tokens, and said rectilinear path of each of said plurality of computing elements being substantially parallel to the rectilinear paths of the others of said plurality of computing elements.

2. A manual computing device as claimed in claim 1 wherein there are six tokens in said first group of said tokens.

3. A manual computing device as claimed in claim 2 wherein each of said tokens in said first group has a color different from the color of the other tokens in said first group, said colors-being yellow, red, white, blue, brown and black, and wherein said tokens are arranged along a rectilinear path with their colors in the order given.

4. A manual computing device including in combination in a common frame a plurality of computing elements each comprising:

a. a rod supported at its ends;

b. spaced means intermediate said ends of said rod dividing the length of said rod into at least three contiguous physically distinct portions;

c. a plurality of apertured tokens mounted on said rod with said rod passing through the apertures thereof whereby said tokens may be moved along said rod, at least four and no more than five of said plurality of tokens being located in the middle one of said three physically distinct portions, at least four and no more than six of said plurality of tokens being located in an end one of said three physically distinct portions, and at least three but no more than four of said plurality of tokens being located in the other end one of said three physically distinct portions;

with the rods of said computing elements substantially parallel to each other.

5. A manual computing device as claimed in claim 4 including in combination in a common frame a pair of abaci comprising tokens mounted on rods, said rods of said abaci being continuations of said parallel rods.

6. A manual computing device as claimed in claim 5 wherein said abaci are of the soroban type.

7. A manual computing device as claimed in claim 4 wherein said spaced means intermediate said ends of each of said rods divides the length thereof into at least four physically distinct portions in addition to said three contiguous portions and with said three contiguous portions at one end thereof, at least four and no more than five of said plurality of tokens being located in the portion next adjacent said three contiguous portions, at least one and no more than two of said plurality of tokens being located in a portion contiguous with said next adjacent portion, at least four and no more than five of said plurality of tokens being located in a further portion next adjacent said two contiguous portions, and at least one and no more than two of said plurality of tokens being located in a portion contiguous with said further portion.

8. A manual computing device as claimed in claim 7 wherein said spaced means intermediate said ends of each of said rods provide three additional physically distinct portions of the length thereof each of said additional portions of each rod having a single token located thereon, the first of said additional portions being interposed between said three contiguous portions and said next adjacent portion, the second of said additional portions being interposed between said portion contiguous with said next adjacent portion and said further portion, and the third of said additional portions being contiguous with said portion which is contiguous with said further portion.

9. A manual computing device as claimed in claim 8 wherein ten rods are included in combination and said single tokens on each rod in one of said additional lengths thereof are colored red, white, blue, brown, black, pink, purple, orange, green and yellow, respectively, in that order beginning from the right.

10. A manual computing device as claimed in claim 4 wherein ten computing devices are included in combination and the rods thereof are colored red, white, blue, brown, black, pink, purple, orange, green and yellow, respectively, in that order beginning from the right.

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1. A manual computing device including in combination in a common frame a plurality of computing elements, each of said computing elements comprising a plurality of movable tokens arranged in three discrete groups, said tokens of each group being mounted for movement toward and away from the others of said groups within a discrete length of a rectilinear path common to all of said tokens of said element, the fIrst of said groups including at least four and no more than six of said plurality of tokens, the second of said groups including at least four and no more than five of said plurality of tokens, the third of said groups including at least three and no more than four of said plurality of tokens, said second group of tokens being interposed between said first group and said third group of tokens, and said rectilinear path of each of said plurality of computing elements being substantially parallel to the rectilinear paths of the others of said plurality of computing elements.
 2. A manual computing device as claimed in claim 1 wherein there are six tokens in said first group of said tokens.
 3. A manual computing device as claimed in claim 2 wherein each of said tokens in said first group has a color different from the color of the other tokens in said first group, said colors being yellow, red, white, blue, brown and black, and wherein said tokens are arranged along a rectilinear path with their colors in the order given.
 4. A manual computing device including in combination in a common frame a plurality of computing elements each comprising: a. a rod supported at its ends; b. spaced means intermediate said ends of said rod dividing the length of said rod into at least three contiguous physically distinct portions; c. a plurality of apertured tokens mounted on said rod with said rod passing through the apertures thereof whereby said tokens may be moved along said rod, at least four and no more than five of said plurality of tokens being located in the middle one of said three physically distinct portions, at least four and no more than six of said plurality of tokens being located in an end one of said three physically distinct portions, and at least three but no more than four of said plurality of tokens being located in the other end one of said three physically distinct portions; with the rods of said computing elements substantially parallel to each other.
 5. A manual computing device as claimed in claim 4 including in combination in a common frame a pair of abaci comprising tokens mounted on rods, said rods of said abaci being continuations of said parallel rods.
 6. A manual computing device as claimed in claim 5 wherein said abaci are of the soroban type.
 7. A manual computing device as claimed in claim 4 wherein said spaced means intermediate said ends of each of said rods divides the length thereof into at least four physically distinct portions in addition to said three contiguous portions and with said three contiguous portions at one end thereof, at least four and no more than five of said plurality of tokens being located in the portion next adjacent said three contiguous portions, at least one and no more than two of said plurality of tokens being located in a portion contiguous with said next adjacent portion, at least four and no more than five of said plurality of tokens being located in a further portion next adjacent said two contiguous portions, and at least one and no more than two of said plurality of tokens being located in a portion contiguous with said further portion.
 8. A manual computing device as claimed in claim 7 wherein said spaced means intermediate said ends of each of said rods provide three additional physically distinct portions of the length thereof each of said additional portions of each rod having a single token located thereon, the first of said additional portions being interposed between said three contiguous portions and said next adjacent portion, the second of said additional portions being interposed between said portion contiguous with said next adjacent portion and said further portion, and the third of said additional portions being contiguous with said portion which is contiguous with said further portion.
 9. A manual computing device as claimed in claim 8 wherein ten rods are included in combination and said single tokens on each rod in one of said additional lengths thereof are colored red, white, blue, brown, black, pink, purple, orange, green and yellow, respectively, in that order beginning from the right.
 10. A manual computing device as claimed in claim 4 wherein ten computing devices are included in combination and the rods thereof are colored red, white, blue, brown, black, pink, purple, orange, green and yellow, respectively, in that order beginning from the right. 